Longy School of Music of Bard College
Music Theoryfor young students
designed for use in Creative Music Theory classes in the Preparatory Division
by John MorrisonEmily Romm
Jeremy Van BuskirkVartan Aghababian
Levels 4, 5, 6
first revisionfall 2011
© 2011 Longy School of Music of Bard College
IntroductionDear student!
As we continue to study music theory, we focus more on some aspects of vertical and horizontalorganization of music; more precisely, we continue to study homophonic and polyphonictechniques and styles. Music that you play mostly belongs to the “common practice period”, aterm that describes music written between 1600 and 1900. At this time tonal music (with tonic asa strong center of a mode) was developed.
Early polyphonic music is modal, i.e. written in modes other than traditional major and minor;therefore modes (Greek or church) will be our focus. Studying modes calls for broadening ourperspective on chords, and in addition to primary chords ( l, lV, V) other chords will beintroduced – II, III, VI, and VII.
We are going to expand our chordal harmony to seventh chords, and learn all types of seventhchords and their inversions, as well as their practical use.
Polyphony will be studied in more or less chronological order: we will listen, analyze, and createpolyphonic pieces using first, second, and third species counterpoint.All of the above components of music theory will be studied using authentic music examples.
In theory 1 – 3 we studied elementary music forms, which are building blocks for larger formssuch as variations, rondo, sonata-allegro. In Levels 4 – 6 we will continue the study of form. Wewill learn the distinction between music form and music genre, and apply our knowledge toanalysis and composing of musical pieces.
Dear parents,
At this level many of your children are more advanced music theory learners, and most likely,able to study independently. There are many theory components that will still benefit from yourparticipation. Your children are learning two - part singing, and you may assist them in eitherplaying or singing one of the parts. They will be composing counterpoints in different clefs, andyou may help them to perform it. They may be harmonizing a melody in different styles, which,again, calls for ensemble playing. And if you feel that your music proficiency is not up to theory4 – 6 standards, you at least can be an appreciative listener.
As your child grows older, don’t miss a chance to listen to music together and discuss it.Music theory applied to their repertoire may be a productive discussion topic.Theory 4 – 6 goes beyond techniques into the field of understanding music in cultural context;your input as a competent or novice listener is very valuable. Enjoy this journey, make music aparticipatory experience for you and your child!
P.S. It is even more essential for theory 4 – 6 students to have a keyboard at home for practicingfour voice leading; please, make sure your child has one.
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Texture, Style, and CounterpointStyle in music.
You’ve heard the word “style” many times in your encounters with music. It could be a style of acertain epoch, or a style of a specific composer, or a style of a performance.
Sometimes the word style is referred to a specific texture of music: polyphonic style orhomophonic style. We have discussed these terms in book 1, but back then we referred to themas texture. It is indeed a texture of music that was preferred in a certain time period; therefore thesame words apply to texture and style.
Monophony
Early Western music (music written down using music notation) was monophonic – a singlemelody sung solo or in unison. It was used for chanting holy texts, and was called a plainchant,plainsong, or Gregorian chant. Plainchant was not metered, and it was constructed using smallintervals, convenient for singing.
Polyphony
Many centuries later musicians started to experiment with adding other melodic lines to it, whicheventually brought the development of polyphony. Polyphony is a texture where independentmelodic lines are combined. The earliest polyphony in Western music was strictly regulated.Rules and regulations of polyphony were compiled in the book Gradus ad Parnassum byAustrian composer and theoretician Josef Fux in 1725. In this book he presented the rules forspecies counterpoint – a teaching tool still used by musicians to study counterpoint.
Counterpoint
Counterpoint literally means note against note. The base melody used for writing a counterpointis called cantus firmus, a fixed melody. Cantus firmus is a plainchant, usually written in alto cleffor tenor part. Cantus firmus has to be sung, therefore the contour and register of a melody has tobe convenient for singing. Appendix 1 contains guidelines for writing a cantus firmus.
Counterpoints vary in their complexity. First species counterpoint is note against note, secondspecies is two against one, third is four against one, and fourth is written in syncopated notes.Fifth species counterpoint is a combination of all four.
See Appendix 1 for a full description of the rules for species counterpoint.
Early music used a variety of modes, not only major and minor that we mostly use in music ofthe “common practice period” (1600 – 1900).
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Modes
Modes are sometimes called Greek, because they were described in Greek treatises on music;they are also called church or medieval modes, because they were used in religious and secularmusic in medieval times; sometimes diatonic, because they can be constructed by starting ondifferent degrees of the major scale.
There are seven modes. You will find both descriptions and examples of each in Appendix 2.
A very important aspect of counterpoint is the smooth movement of voices. Composers ofcommon practice period were all trained in counterpoint. Eventually it brought the formation ofchords and the development of homophonic style, or homophony.
Homophony
Homophony is a texture (and a style) where a leading voice (homo- one, phon- voice) issupported by accompaniment (harmony).
Chorale texture, where all voices move basically together as a block chord, emphasizing the topvoice as melody, is also homophonic texture.
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HarmonyHarmony in music has several meanings.
1. Musical pitches sounding together.
2. A branch of music theory formalizing relations between pitches in melody, chords andkeys.
The building blocks of polyphony are intervals; the building blocks of harmony are chords.
Chords
A chord is made of a minimum of three pitches, chords separated by thirds are called tertian.
In classical harmony, the most commonly used chords are triads and seventh chords. In Levels 1- 3 we discussed triads, their inversions and a seventh chord – the dominant seventh.
Seventh chords
Seventh chords may be constructed on any note in a scale by adding another third on top of atriad. The official name of each seventh chord comes from this concept of building: we name theseventh chord by the quality of its triad and the quality of its seventh. Read each name belowfrom the bottom up so that you name the triad first.
Depending on their location in a key they have different structure and function.
Dominant seventh chords
The most common seventh chord is the dominant seventh – an extension of the dominant triad.This chord is constructed with a major triad plus a minor seventh above the root.
Its official name is major-minor seventh chord, but the name most generally used is dominantseventh. This is because only one major-minor seventh chord normally occurs in either major orminor, and it is on the dominant scale degree.
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Inversions of seventh chords
Seventh chords are inverted the same way intervals are inverted, by bringing a bottom sound of achord one octave up and putting it on top of a chord. The example below includes the numeralswhich show all the intervals above the bottom note.
Naming inversions
Inversion names include the official name of the root or triad (dominant or V, supertonic or ii,etc.) with arabic numerals giving the location of chord members above the note that is in thebass. The example below provides the commonly-used symbols for dominant seventhinversions.
Resolution of seventh chords
Seventh chords combine stable and non-stable tones. The number of non-stable tones included inchord influences its character and intensity. When seventh chords are resolved, non-stable tonesare brought to stable tones. Resolution of the dominant seventh and its inversions demonstrateshow this happens. (Every tone in the dominant seventh has a strong tendency to go to a specificplace. A root-position one will resolve to a tonic with three roots and one third. Note how theinversions are able to resolve to complete tonic triads by keeping scale degree 5 as a commontone.)
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Diminished seventh chord
Another non-stable chord is vii07, which occurs in harmonic minor. This chord has a diminishedtriad and a diminished 7th above its root. Officially, it is called a diminished-diminished seventhchord, but diminished seventh is a widely-used name for it.
Resolution of diminished seventh chord
A diminished seventh chord consists of two diminished fifths. Resolving each of the diminishedfifths correctly brings us to a modification of a tonic triad, which has a doubled third.
Other seventh chords
A seventh chord on the second scale degree in minor or on the leading tone in major has adiminished triad and a minor seventh above its root. It is generally known as a half-diminishedseventh chord, though the official name is diminished-minor seventh.
A seventh chord on scale degree 1 or 4 in major or on scale degree 3 or 6 in minor has a majortriad and a major seventh above its root. Its official name is major-major seventh, but majorseventh chord is its common name.
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A seventh chord on scale degree 1 in minor has a minor triad and a minor seventh above its root.Officially, it is a minor-minor seventh, but minor seventh chord is its common name. There areminor sevenths to be found elsewhere in major and minor keys. Try to figure all possiblecombination of triads and intervals of the seventh to make all the seventh chords in a key.
The most commonly used seventh chords are dominant seventh, diminished seventh, and half-diminished seventh chords.
Resolving or connecting seventh chords requires knowledge of four-part harmony. In four-partharmony all chords, even triads, have to have four notes.
Four part harmony
In polyphony voices have independent contours and rhythm, in homophonic style they movetogether in the same rhythm. Because homophony is a product of polyphony, the smoothconnection between chords or voice leading is very important, and the aim of every line createdis to be musically interesting.
Voice leading
The movement of each voice from one chord to the next is called voice leading. There are fourparts in traditional harmony. They get their names from voices in chorus: soprano, alto, tenor,bass. Notice how the stems of voices which share a staff go in opposite directions.
In levels 1 - 3 we used three part chords, now one member of the chord (frequently the bass) ispresent twice in a chord, or doubled, to make a fourth part. Knowing which triad member todouble is important. In general, doubling the tonal scale degrees (1, 4, 5, and sometimes 2: thosescale degrees which do not change according to mode) will almost always work well. Achievinggood melodic lines in voice leading is sometimes more important than doubling the “correct”triad member. Find and identify the chord member that is doubled in the example above.
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Chords may be in close or open position, which alters the sound to some degree but doesn'tchange the chord quality.
Close chord position
When notes in a chord are spaced as closely as possible it is called close chord position. Thechord could have a root, third, or fifth in the soprano part, it doesn't matter.
Open chord position
When the notes of a chord are more spread out (again, having any chord member on top) it is anopen chord position.
Rules of voice leading
For a complete description of movement types and voice-leading, see Appendix 3.
Real music rarely exists in the form of four part harmony. Usually a melodic line has notes thatdo not belong to a harmony, and they are called non-harmonic tones, or non-chord tones.
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Non-harmonic tones (non-chord tones)We will classify non-harmonic tones by their location in a measure. Non-harmonic tones arenotes that do not belong to the triad or seventh chord active at the time. Non-harmonic tones arestrictly governed according to how they are introduced (prepared) and how they move to chordtones (i.e., how they are resolved).
Weak beat non-harmonic tones
Passing tone (PT): a non-chord tone between two different harmonic tones. Passing tones mustresolve by step in the same direction they are introduced.
Neighbor tone – upper neighbor (UN) or lower neighbor (LN): a note step higher or lowerbetween the same repeating harmonic tone.
Anticipation (ANT): when a tone of the next chord sounds before the chord which contains it.Note that anticipations generally require a change of harmony.
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Strong beat non-harmonic tones
Accented passing tone (PT): passing tone on a strong beat, or the strong part (first part) of a beat.
Suspension (SUS): a tied or repeated note from previous chord. The non-chord tone is preparedby belonging to the previous chord, and is held while the chord changes. When the tone does notbelong to the new chord, it is a dissonance, and must resolve down by step. Note that the arabicnumeral below the bass shows the interval movement of the dissonance and its resolution.
Appoggiatura (APP): non-harmonic tone appears as a leap in the melody. Typically, the leap isup, and the non-chord tone will resolve down by step.
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Other non-harmonic tones
There is also an escape tone (ET), a weak-beat non-harmonic tone between two consonances thatare a step apart, that skip by a third into resolution. One may describe this action as approachingthe dissonance (non-chord tone) by step, left by leap in the opposite direction.
Cambiata, CAMB, a weak beat non-harmonic tone connecting two consonances that are a stepapart. The dissonance is approached by leap and left by step in the opposite direction.
A neighbor group (NG), or double neighbor tone (DN), which is sometimes referred to as achanging tone, is a combination of upper and lower neighbor tones. Note that in the examplebelow, the chord tone is not sounded between the two non-chord tones. Some people would callthis an incomplete neighbor group.
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Diatonic chords and functional progressionsIn medieval and renaissance music, the interaction of lines and intervals is most important, andany chord could follow any other. In common-practice period, some chords acquired specialsignificance, especially in providing a sense of forward movement. Tonic (T) is beginning andend, dominant (D) leads to tonic, and subdominant (S) leads to dominant. The three chords standfor their functions in harmonic progression, which are tonic, dominant, and pre-dominant. Whenchords function in this way, we say it has functional harmony.
Tonic function chords include I (or i) and on occasion the chords which share two notes withtonic, iii (III) or vi (VI). Returning to tonic is the eventual goal of all common-practice periodmusic. (Chords in parentheses come from the minor mode.)
Dominant function chords include V, V7, and vii0. (Notice that these chords are the same inmajor and minor. The functional dominant in minor is spelled using harmonic minor.)
Pre-dominant chords include IV (iv), ii (ii0), and seventh chords built upon them.
Supertonic triad
A triad constructed on scale degree 2, the supertonic leads most frequently to the dominant triad,and therefore has pre-dominant function. The chord is minor (ii) in a major key, and diminished(ii0) in a minor key.
Mediant triad
A triad constructed on the third scale degree combines sounds belonging to the tonic triad and thedominant triad, and can occasionally stand in their place. It is called mediant, because it isequally removed from T and D. The mediant is minor (iii) in the major keys, and can be eithermajor (III) or augmented (III+) in a minor key. The augmented quality comes from a raisedleading tone, which explains its occasional use as a dominant-function triad.
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Submediant triad
A triad constructed on the sixth scale degree combines sounds of S and T triad, and can thereforesometimes take on either function, tonic or subdominant. It is called submediant, because it isequally removed from S and T.
Leading tone triad
In major and in harmonic minor a triad on the seventh scale degree is diminished (vii0); asmentioned above, it is a chord of dominant function.
Subtonic triad
The triad constructed on the seventh scale degree in natural minor is major (VII, often referred toas bVII). In minor keys, it is the relative major of dominant minor, and the dominant of therelative major.
Primary and secondary chords
Triads constructed on first, fourth, and fifth degrees or, T, S, and D are called primary triads. Allother triads are secondary. Notice that in major mode primary triads are major, and secondarytriads are minor. In minor mode primary triads are minor (when spelled using the natural minor),and secondary triads are major.
Using primary and secondary triads creates unexpected harmonic combinations, enriches musicwith more colors.
Relationships between primary and secondary chords
Primary and secondary chords are closely related. In major mode, the submediant is the relativeminor of tonic, while the mediant is the relative minor of dominant, and supertonic is the relativeminor of subdominant.
In minor mode, the mediant is the relative major of tonic, submediant is the relative major ofsubdominant, and subtonic is the relative major of dominant minor.
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Secondary and primary triads in harmonization
The ambivalent character of secondary chords allows for their wide use in harmonization.Primary triads are used in structurally significant places: in the beginning of a piece forestablishing a key, and in cadences.
Types of cadences
In levels 1 – 3 we discussed melodic cadences, now we are going to focus on cadences expressedin harmony. Cadences function like punctuation, they shape musical phrasing.
There are four basic cadence types:
Authentic (full) cadence (AC): usually at the end of a phrase.
An authentic cadence is called perfect if the soprano carries scale degree 1 in the tonic chord, andboth dominant and tonic are in root position. We abbreviate the label as PAC. An authenticcadence is imperfect when it has 3 or 5 in the tonic chord, one of the chords is inverted, or theleading-tone chord is used instead of dominant. We abbreviate the label as IAC.
Half cadence (HC): cadence on dominant, creates a need for answering in full cadence.
Plagal cadence (PC): S-T, usually at the end of a phrase, most frequently after a full cadence.
Deceptive cadence (DC): D – vi (VI in minor)), prolongs music, calls for a full cadence.
In addition to bringing pieces or sections to close in the home key, cadences are places that makea change of key more firm, a process known as modulation.
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Modulation and chromaticismModulation is a change of key confirmed by cadence. Key change occurs very often in music,especially in longer pieces. Sometimes a change of key is just hinted before returning to an initialkey. This is called tonicization.
Tonicization
Sometimes a tone in a key assumes the potential of a new tonic. It happens with help of a newleading tone which points to that tonic. A leading tone lies a half-step below its tonic, whichoften leads to the presence of a note that does not belong to the original key of the piece. It is theaural strength of the accidental that creates the feeling of a new potential tonic.
Secondary dominant
Any chord in a scale may be preceded by its own dominant. We know that a dominant chord ismajor, and that its third is the leading tone of a key. The dominant may be a dominant seventhchord as well, which occurs only one place in a scale, and which might bring additionalaccidentals. This new dominant has different names – secondary, applied, or transient dominant.
Notice in the example below that we label secondary dominants as “of” the chord whose root hasthe new leading tone. We will soon see that a composer might change the key for a while to thenew tonic, and it will be either major or minor based upon whether the chord built on it is majoror minor.
Chromaticism
There are 12 notes in a chromatic scale, it is constructed by using all semitones in an octave. Oneway to think of the chromatic scale is as a succession of diatonic notes in a scale with leadingtones to each diatonic note. Any time a note appears that is not contained in the key of a piece,we call that chromaticism. Some chromaticism simply ornaments a note. When chromaticismfunctions as part of new key being established through tonicization or modulation, it will besupported harmonically. (See the example on the next page.)
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Tonicization and modulation
When after tonicization a new key is confirmed (by a cadence in the new key), modulationoccurs. In the example below, the previous example has been extended, but rather than come torest on a half-cadence in the original key of a minor, the succeeding chords belong to the newkey, d minor.
Role of modulation
Changing keys makes music more dynamic; it creates boundaries between different parts inlarger musical pieces. It allows a composer to use melodies and motives in many ways withoutour growing weary of them.
Making modulation
Modulation is usually made through using a common note in a melody or a common chord (orseries of chords) in a harmony that assumes a new identity in a new key. In the example above,notice how the d minor chord on beat three of the first measure can belong to both a minor and dminor. It is therefore a common chord, or pivot.
A common chord is called pivot chord. After a pivot chord, cadence confirming a new keycompletes a modulation.
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Types of modulations
Modulations could be smooth, using one or a few pivot chords. This type is known as common-chord modulation.
It could be an abrupt modulation, introducing different keys without any preparation (starting adifferent part in a different key). When abrupt modulation occurs between two phrases, somecall it a phrase modulation.
A composer might reduce the texture to a single note, such as scale degree 2, and move ahead ina key that treated that note as tonic. This would be an example of common-tone modulation.
A modulation could lead to a key that shares all notes with the original key (as in modulation tothe relative major or minor), or to a key that has no common notes with the original key.
Closely related keys
Keys are related according to the number of notes they have in common. The more notes a pairof keys have in common, the more chords they will have in common. Consider G major and Cmajor. Only one note is different, but it shifts the tonic and all harmonic relations. The examplebelow shows the chords the two keys have in common.
Relative major and minor are the closest, they share all notes.
Keys are considered closely related if they are one accidental away in the circle of fifths. Theexample above is of two chords a fifth apart in the circle of fifths.
Therefore, closely related keys will be keys ofprimary chords and their relative keys. This producesa set of closely-related keys which includes all themajor or minor chords in a key (i.e. not includingdiminished triads.)
Notice that in the chart to the right, all the scale stepsof C major (except the leading tone, which wouldcarry a diminished triad) are either one step away inthe circle of fifths, or are relative minors of a key thatis one step away. All of the chords (= keys) diatonicto a major key are quite closely related.
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Tonal plan
Different sections of music are often in different keys, and the different keys all are related insome way back to the original tonic. A tonal plan shows the changing keys within a piece.
Tonal counterpoint
Tonal counterpoint is eighteenth-century or Baroque style counterpoint. It is driven by harmony,and therefore combines understanding of harmonic relationship on a larger scale, and some rulesof species counterpoint. Tonal counterpoint is a technique of composing specific genres ofpolyphonic music: invention, round, fugue. It is also technique of polyphonic development usedby later composers for creating parts of classical forms.
Form, genre, and style in musicThe previous sections of the book explained ways of presenting and developing musical ideasand images; this section explains how music is structured and classified. Music is the mostephemeral of arts; it only exists at the time of performing. Why does it have to be structured, andwhat does structure in music mean?
Structure in music
Music, like literature, or film, is a form of art that develops in time. Music listeners andperformers have to be able to comprehend music while it sounds. Structuring musical ideas intime is the function of music form. Form in music is a way of organizing multiple musicalcomponents to make it easier for our brain to recognize, retain, and process musical ideas.
Graphic expression of music form
Musical form is not a visible structure, but it could be expressed through graphics. Let’s try topresent “Twinkle, twinkle, little star” using graphical symbols.
There are three phrases in a song, the first and the last have the same words, and appear with thesame music. In a graphic scheme it can be presented with the same symbol, in this case, with theletter A.
The middle part, “Up above the world so high, like a diamond in the sky”, has a differentmelody, and is presented with a different letter B.
The graphic scheme for this song is ABA. The song has three sections, and is written in ternary(three-part) form.
Some characteristics of musical form
Most musical forms are sectional, with the exception of forms that cannot be divided.
Sectional forms are often named by the number of sections they present: binary, ternary, roundedbinary.
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Sections in music are used at micro- and macro-levels. Twinkle, twinkle, and a three-movementsymphony are both composed in ternary form.
Some forms emphasize development of musical ideas more than other forms; these aredevelopmental forms. Sonata allegro is an example of a developmental form.
Some forms focus more on improvisation; these are improvisational forms. Rhapsody is anexample of improvisational form.
Hierarchy of musical form
The building block of musical form is the motive. Motive is a short musical idea, a recurringpattern, pitch, or rhythm.
Motives are used in making a phrase, which is a musical statement that has a beginning, middle,and end.
Two or more phrases may create a musical period. A period is created when phrases are groupedtogether by cadences, the final one being stronger than those which came before.
In the song “Twinkle, twinkle little star” section A (above) is a period, which is a section in theternary form.
Periods, or other means of organizing music, create larger forms. Modulation is very importantin creating larger forms, and return of tonic is an essential part of full closure in a large piece.
Forms of classical music
Commonly used forms of classical music are:
Binary –AB, AA, AA'
Ternary – ABA, AA'A
Rounded binary – AABA, ABA'
Ternary and rounded binary are actually very similar, since both feature departure (contrast) andreturn (recall). Ternary has more distinctive contrast, which helps create a stronger feeling ofrecall.
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Variations – a sectional form in which the main theme is embellished and changed.
A A1 A2 A3, etc.
Rondo is composed of alternation of refrain and different episodes ABACADA.
One of the most complex forms of classical music is the form of sonata allegro.
It is a sectional form ABA', where B is a development of the musical ideas from part A.
There are usually two contrasting musical themes in part A, as well as a theme connecting them,and a theme concluding the exposition (that’s how part A is called, as an analogy to a novel,which sonata allegro is often compared with). The themes in sonata allegro are called primaryand secondary, and in the exposition the contrast between them is amplified by presenting themin different keys. In the recapitulation section both themes appear in the tonic key.
Sonata allegro is a musical form; it is also a name of a first movement of a multi-movementsonata form – one of the most important forms of classical music.
Multi-movement, or cyclical forms
Multi-movement forms combine several movements that serve as sections of a larger musicalcreation. Sometimes there is one underlying idea expressed through a theme or a key, whichmakes the multiple movements create a cycle. Sonata, quartet, concerto, and symphony areexamples of multi-movement form.
Sonata, quartet, symphony are also genres of classical music.
Genres in music
Genre is a kind of music. Genre could define the whole area of music – vocal or instrumental; anintended audience – folk, classical; music of specific time – Renaissance, Baroque, modern;social function – religious, court music.
March is a genre of music. Marches have similar musical characteristics: instrumental music, 4/4meter, dotted rhythm. There are different kinds of march: funeral, wedding, military, etc.
Genres of classical music are types of music established during classical era (1750-1850) inEurope : sonata, quartet, symphony, concerto.
Genres of Romantic music are symphonic poem, song cycle, prelude, nocturne, impromptu,etude, etc.
Terms genre and style are sometimes used interchangeably.
Style in music
Style is a sum of musical means particular to a composer (Beethoven’s style), or a specific timeperiod (Baroque style), or to a specific ethnic or regional music (Hungarian folk music,flamenco, salsa). Sometimes, as it has been mentioned before, a style is linked to texture(homophono-harmonic style, polyphonic style).
Knowledge of musical form, genre, and style help musicians and listeners to understand andappreciate music in a cultural context, and provide guidance for interpretation.
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Appendix 1
Species Counterpoint
Counterpoint - “point against point” The interaction of multiple melodic lines is at the heart ofthe study of counterpoint. It is not concerned with chords, but it is concerned with the interplayof consonance and dissonance created when two melodies are played at the same time. Thestudy of species counterpoint has a long history. It was developed out of the compositional styleof sixteenth-century composers like Palestrina. Species counterpoint has been a traditional partof the study of music theory for the last 300 years. Composers such as Bach, Mozart, andBeethoven studied counterpoint to learn how music is constructed. Many of the techniquesdemonstrated in species counterpoint can be seen in tonal music from the Baroque period all theway to today.
The exercises in species counterpoint are designed to help understand how melody and harmonyinteract to create shape and form in music. Species counterpoint gives the basic framework forunderstanding the structure of all tonal music.
There are two principle components in the study of counterpoint. The first component is a set ofrules that govern what is considered a good melody.
Intervallic contentUse primarily stepwise motion.Leaps can only be consonant intervals.Leaps cannot be larger than an octave.After a leap of a P4 or larger, the melody should move by step in the opposite direction.
Melodic structureA melodic phrase has a beginning, middle, and an end.
1. The beginning is introduces the key and always starts on the first, third, or fifthscale degree.
2. The middle of the melody should have an interesting shape and work its way upto a high point. Melodies have only one high point.
3. The end of a melody is the cadence. The cadence signals the end of the phrase.
The second component in the study of counterpoint is the interaction between two (or more)melodies. Every melody will be written against a cantus firmus. Composers in the sixteenthcentury based their compositions on chants (melodies) from the Medieval period. A borrowedchant is called a cantus firmus. They wrote new melodies that complemented these oldermelodies to create their new compositions. The rules that govern the interaction of melodies(counterpoint) are broken into species. Each species becomes progressively more complicated.
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Species 1Rhythm: 1 against 1. Whole note against whole note.
Intervals: Beginning (first interval) – only a third, fifth, or octave.
End – Cadence formula (see page 24)
Only consonant intervals. No dissonant intervals allowed. Parallel fifths and octaves are alsoforbidden. A parallel fifth or octave is the use of two consecutive perfect fifths or octaves.Composers believed this sound destroyed the sense of two individual melodies.
Species 2Rhythm: 2 against 1. Half notes against whole note.
Intervals: Beginning – same as first species.
Middle – the first note of measure (strong beat) must be consonant. The second note can be consonant or dissonant. If it is dissonant, it must be a passing tone. A passing tone is a dissonant interval that resolvesby step in the same direction. The melodic motion must be by step.
End – same as first species.
Parallel fifths and octaves are still forbidden. In second species, parallel fifths and octaves arenot allowed between two consecutive notes. They are also not allowed between consecutivestrong beats (beginning of a measure).
Species 3Rhythm: 4 against 1. Quarter notes against whole note.
Intervals: Beginning – same as first species.
Middle – The first note in the measure must be consonant. The other threenotes can be consonant or dissonant. If they are dissonant, they must be apassing tone or a neighbor tone. The rules for passing tones are the sameas second species. A neighbor tone is a dissonant interval that moves bystep away from a consonant interval and then returns to the previous note.The intervals on both sides of a neighbor tone must be consonant.
End – same as first species.
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Species 4Rhythm: Syncopated half-notes. 2 against 1. The second half-note in the measure
is tied to the first half note of the next measure. A half-rest may begin thecounterpoint line.
Intervals: Beginning – same as first species.
Middle – Fourth species deals with suspensions. It is a three partprocedure. The preparation note (the note on the second half note, the onethat is tied) must be consonant. The tied note may be dissonant orconsonant. If consonant, you can skip to the next tone (it must be aconsonant leap.) When dissonant, a suspension is created, and it mustresolve down by step to become consonant. The three acceptableintervallic patterns for suspension resolution are 7-6, 4-3, and 9-8. Thissuspension pattern should be the primary melodic pattern. Occasionally,the suspension pattern can break by including consonant notes for theentire measure. The tied rhythm should remain consistent, but may bebroken once per exercise. Breaking the series of ties will produce asecond-species measure, so follow those rules in those measures. Incounterpoint written below the cantus firmus, the only allowable intervalpattern is 2-3. (see example)
End – same as first species.
In fourth species, parallel fifths and octaves are not allowed on consecutive weak beats.
Species 5Rhythm: A combination of species 1-4.
Intervals: Beginning – same as first species.
Middle – Fifth species allows creative combinations of species 1-4.Interval rules for each species must be followed when writing in thatspecies. Do not break any species rules when changing from one toanother.
End – same as first species.
CadencesEach species counterpoint exercise must end in a cadence. Each of the following notepatterns is a common melodic cadence based in C. Use one of these cadences to endevery species counterpoint exercise. Transpose the pattern as necessary. (Note: leading-tone should be raised in minor modes.)
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Appendix 2
The Church Modes
Some of the earliest work in music theory had to do with figuring out the scales used inGregorian chant. The result is known today as the church modes. Sharps and flat were unknownin such ancient times, which is nice for the ease of using them today. We can use the pitches ofC major (the C-major pitch set) and simply begin and end on a particular note, and the pattern ofwhole- and half-steps changes. This way of remembering the modes also allows you to sing amode that belongs to a set of pitches from any major scale.
In the table onthe right, you'llnotice that eachmode starts on adifferent scaledegree of Cmajor. Thesame will betrue of any set ofnotes comingfrom a particularmajor key. Forexample, scaledegree 2 to 2using the pitchesof a major keywill produce adorian mode onthat second scaledegree.
Each mode isalso describedhere in terms ofhow it differsfrom either amajor scalestarting on thesame note, or anatural minorscale starting onthe same note.
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Appendix 3
Root Position Voice-Leading Guidelines
Types of Motion
Oblique motion – One voice moves while the other stays the same.
Parallel motion – Both voices move in the same direction keeping the same interval.
Contrary motion – Voices move in the opposite direction.
Similar motion – Both voices move in the same direction arriving on a different interval.
All motion types are important. You should not try to avoid a certain type of motion, in factmixing the types is desirable. You only need to avoid moving by problematic intervals.
Problematic intervals in voice-leading.
Parallel fifths and octaves – parallel motion by fifth or octave between any voice is prohibited.Parallel fifths or octaves destroy the sense of independence between the voices.
Hidden fifths or octaves (direct fifths or octaves) – Hidden fifths occur when the two outervoices move in the same direction (similar motion) and arrive on a perfect fifth or octave. Ahidden fifth or octave is acceptable if the upper voice moves by step. In fact, it would beimpossible to complete an exercise if you could not move to a fifth or octave by step.
Melodic motion – Voices should not move by augmented of diminished melodic intervals.
Voice crossing – Voice crossing occurs when one voice is above or below an adjacent voice.The acceptable place for this to occur is between the alto and tenor. Do not cross soprano or basslines.
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Steps for writing ROOT POSITION VOICE-LEADING exercises.(These steps apply to root position part writing exercises only. Examples using inversions or harmonizing a melodyare based on these rules, but they need more flexibility in their execution.)
1. Write the bass notes for each chord.2. Keep the common tones in the same voice between each chord.
➢ If the roots of the chords are a third or sixth apart, there will be two common tones.➢ If the roots of the chords are a fourth or fifth apart, there will be one common tone.➢ If the roots of the chords are a second or seventh apart, there will no common tones.
3. Move the remaining voices to closest note in the next chord.➢ If there are no common tones (root motion by second or seventh), the upper voices
(SAT) should move in contrary motion to the bass. This will avoid any problematicintervals.
➢ You should almost always double the root (with some exceptions; some people preferto simply double the tonal scale degrees, which are 1, 4, and 5), and each chordshould be a complete. (No chord tones missing. There are also a few exceptions tothis rule. If anything is to be omitted, it is the fifth, not the third.)
Special Considerations:V chord – The leading tone of the key (3rd of the V chord) should always resolve to tonic if it isin an outer voice ( S or B). If the leading tone is in an inner voice, it may resolve to the fifth ofthe tonic triad to complete the chord.
Exceptions:V-vi (deceptive cadence) – This progression has root position by step. The upper voices shouldmove contrary to the bass except the leading tone of the key (3rd of the V chord). This shouldresolve UP to the tonic. The result will be a vi chord with a DOUBLED THIRD (note that thisis scale degree 1).
VI-V in minor keys – Normal voice-leading rules will create a melodic augmented second. Youcan avoid this by doubling the third in the VI chord.
ii-V – It is common to treat this progression as if it has no common tones. In this case the uppervoices move in contrary motion to the bass. In a major key, you can use either normal rules ormove the upper voices in contrary motion. If the progression occurs in root position in a minorkey, you must move the upper voices in contrary motion to the bass. (This is a rare occurrence,since the diminished triad almost always uses first inversion.)
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Appendix 4
Table of Non-Chord Tones
name (abbreviation) approached by left by commentspassing tone (p) step step in same direction may be on or off beat
neighbor (n) step step in opposite direction
suspension (s) same tone down by step harmony changes tocreate dissonance, noteprepared by belonging toprevious harmony
retardation (r) same tone up by step harmony changes tocreate dissonance, noteprepared by belonging toprevious harmony
appoggiatura (app) leap or step step, typically down on the beat
escape tone (e) step leap in opposite direction
neighbor group (n.gr)
step step an upper and lowerneighbor paired
anticipation (ant) step (typically) orleap
same tone anticipates comingharmony
pedal point (ped) same tone same tone note sustains whileharmony changes
